<p> Revisit ODE solvers as integrators </p>

f11ddb25-bc40-4494-b796-b6cd434c983f 8 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Test function x f x sqrt exp :

4 appVersion 0.98.6179.21440 ≡

x Y D x f :

a 0 : b 2 : 12 mat

sol 0 a b 10000 x Y D al_rkckadapt :

exact 5.40752818465627

very good ! sol sol rows row 2 5.40752818457808 12 mat

sol 0 a b 10000 x Y D rkfixed :

3 ½ D sol sol rows row 2 5.40722 12 mat

x f x 0.5 1 -^x - exp * eval : a 1015 -^: b e : 12 mat 21 sys

x Y D x f :

fails ! sol 0 a b 10000 x Y D dn_GearsBDF :

π sqrt b sqrt erf * 1.73750207472565

sol sol rows row 2.7183 1.7382 12 mat

sol 0 a b 10000 x Y D rkfixed :

f....n freak ! sol sol rows row 2.7183 8597.6753 12 mat

sol 0 a b 10000 x Y D al_rkckadapt :

4 ½  D sol sol rows row 2.71828182845905 1.7375246742603 12 mat

u b 0 u 2 - ≤ 16 / 2 u + (3^* 2 - u ≤ (u 1 - ≤ (& 16 / 2 u + (3^* 23 / 1 u + (3^* - 1 - u ≤ (u 0 ≤ (& 23 / 1 u - (3^* - 16 / 2 u - (3^* + 0 u ≤ (u 1 ≤ (& 16 / 2 u - (3^* 1 u ≤ (u 2 ≤ (& 0 cases :

known exact u b u 2 - 2 int 1.000000000000000

x Y D x b :

4 ½ D sol 02 - 210000 x Y D dn_GearsBDF :

sol sol rows row 1.99999999999969 0.999920601698221 12 mat

rkfixed  exact! sol 02 - 2100 x Y D rkfixed :

sol sol rows row 2.000000000000000 1.000000000000000 12 mat

sol 02 - 210000 x Y D al_rkckadapt :

slow but converges exact sol sol rows row 2 0.999999999999998 12 mat

Useless solvers. # # # # # al_rkckadapt # # # # # dn_AdamsMoulton # # # # # dn_ExplicitRK45 # # # # # dn_GearsBDF # # # # # dn_ImplicitRK5 51 line

ONE  possible limited solver. # # # # # mwode113 # # # # # mwode15s # # # # # mwode23 # # # # # mwode23s # # # # # mwode45 51 line

# # # # # Rkadapt # # # # # rkfixed # # # # # rkm9mka # # # # # rkm9mkn # # # # # rkm9st 51 line

# # # # # mk52lfa # # # # # mk52lfn 21 line